Uniqueness and non degeneracy of positive solutions for critical exponent problem in R^2

(TIFR CAM, BANGALORE, INDIA)

Abstract. Brezis raised the question of uniqueness of positive solutions of criticalexponent problem in a Ball. This problem was settled in dimensions greater than orequal to three. It was an open problem in two dimensions because of ineffectiveness ofPohozaev's identity and the critical exponent is of exponential nature. In this talk we willprove that the solutions are unique and non degenerate in balls of small radius for alarge class of non linearities.